Simplify the following expression: $ z = -1 + \dfrac{9x - 1}{3} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-1}{1} \times \dfrac{3}{3} = \dfrac{-3}{3} $ Therefore $ z = \dfrac{-3}{3} + \dfrac{9x - 1}{3} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-3 + 9x - 1}{3} $ $z = \dfrac{9x - 4}{3}$